Project Description

Now in the second portion of the class, we’re going to analyze the ToothGrowth data in the R datasets package.

1 - Load the ToothGrowth data and perform some basic exploratory data analyses

2 - Provide a basic summary of the data.

3 - Use confidence intervals and/or hypothesis tests to compare tooth growth by supp and dose. (Only use the techniques from class, even if there’s other approaches worth considering)

4 - State your conclusions and the assumptions needed for your conclusions.

Some criteria that you will be evaluated on

Did you perform an exploratory data analysis of at least a single plot or table highlighting basic features of the data?
Did the student perform some relevant confidence intervals and/or tests?
Were the results of the tests and/or intervals interpreted in the context of the problem correctly?
Did the student describe the assumptions needed for their conclusions?

1 - Load the ToothGrowth data and perform some basic exploratory data analyses

ToothGrowth {datasets}

The Effect of Vitamin C on Tooth Growth in Guinea Pigs

Description

The response is the length of odontoblasts (teeth) in each of 10 guinea pigs at each of three dose levels of Vitamin C (0.5, 1, and 2 mg) with each of two delivery methods (orange juice or ascorbic acid).

Usage

ToothGrowth

Format

A data frame with 60 observations on 3 variables.

[,1] len numeric Tooth length

[,2] supp factor Supplement type (VC or OJ).

[,3] dose numeric Dose in milligrams.

Source

C. I. Bliss (1952) The Statistics of Bioassay. Academic Press.

References

McNeil, D. R. (1977) Interactive Data Analysis. New York: Wiley.

library(datasets)
data(ToothGrowth)
dim(ToothGrowth)

## [1] 60  3

head(ToothGrowth)

##    len supp dose
## 1  4.2   VC  0.5
## 2 11.5   VC  0.5
## 3  7.3   VC  0.5
## 4  5.8   VC  0.5
## 5  6.4   VC  0.5
## 6 10.0   VC  0.5

2 - Provide a basic summary of the data.

summary(ToothGrowth)

##       len        supp         dose      
##  Min.   : 4.20   OJ:30   Min.   :0.500  
##  1st Qu.:13.07   VC:30   1st Qu.:0.500  
##  Median :19.25           Median :1.000  
##  Mean   :18.81           Mean   :1.167  
##  3rd Qu.:25.27           3rd Qu.:2.000  
##  Max.   :33.90           Max.   :2.000

c(round(mean(ToothGrowth$len),3) , round(sd(ToothGrowth$len),3),round(var(ToothGrowth$len),3))

## [1] 18.813  7.649 58.512

ToothGrowth$dose <- as.factor(ToothGrowth$dose)
summary(ToothGrowth)

##       len        supp     dose   
##  Min.   : 4.20   OJ:30   0.5:20  
##  1st Qu.:13.07   VC:30   1  :20  
##  Median :19.25           2  :20  
##  Mean   :18.81                   
##  3rd Qu.:25.27                   
##  Max.   :33.90

3 - Use confidence intervals and/or hypothesis tests to compare tooth growth by supp and dose. (Only use the techniques from class, even if there’s other approaches worth considering)

Graphical analysis of data:

library(ggplot2)

ggplot(ToothGrowth,aes(x=factor(dose),y=len,fill=factor(dose))) + 
    geom_boxplot(notch=F) +
    facet_grid(.~supp) +
    scale_x_discrete("Dosage (mg)") +   
    scale_y_continuous("Tooth Length") +  
    scale_fill_discrete(name="Dose (mg)") + 
    ggtitle("Effect of Supplement Type and Dosage on Tooth Growth")

The condifence intervals (95%) are:

x <- ToothGrowth$len[ToothGrowth$supp=="OJ" & ToothGrowth$dose == 0.5]
y <- ToothGrowth$len[ToothGrowth$supp=="VC" & ToothGrowth$dose == 0.5]
d05 <- c(round(mean(x),2),
  (round(mean(x) + c(-1,1) * qnorm(0.975) * sd(x)/sqrt(length(x)),2)),
  round(mean(y),2),
  (round(mean(y) + c(-1,1) * qnorm(0.975) * sd(y)/sqrt(length(y)),2)))

x <- ToothGrowth$len[ToothGrowth$supp=="OJ" & ToothGrowth$dose == 1]
y <- ToothGrowth$len[ToothGrowth$supp=="VC" & ToothGrowth$dose == 1]
d10 <- c(round(mean(x),2),
  (round(mean(x) + c(-1,1) * qnorm(0.975) * sd(x)/sqrt(length(x)),2)),
  round(mean(y),2),
  (round(mean(y) + c(-1,1) * qnorm(0.975) * sd(y)/sqrt(length(y)),2)))

x <- ToothGrowth$len[ToothGrowth$supp=="OJ" & ToothGrowth$dose == 2]
y <- ToothGrowth$len[ToothGrowth$supp=="VC" & ToothGrowth$dose == 2]
d20 <- c(round(mean(x),2),
  (round(mean(x) + c(-1,1) * qnorm(0.975) * sd(x)/sqrt(length(x)),2)),
  round(mean(y),2),
  (round(mean(y) + c(-1,1) * qnorm(0.975) * sd(y)/sqrt(length(y)),2)))

1 - dosage 0.5 mg

OJ-mean OJ-lower OJ-upper VC-mean VC-lower VC-upper

## [1] 13.23 10.47 15.99  7.98  6.28  9.68

2 - dosage 1.0 mg

OJ-mean OJ-lower OJ-upper VC-mean VC-lower VC-upper

## [1] 22.70 20.28 25.12 16.77 15.21 18.33

3 - dosage 2.0 mg

OJ-mean OJ-lower OJ-upper VC-mean VC-lower VC-upper

## [1] 26.06 24.41 27.71 26.14 23.17 29.11

4. State your conclusions and the assumptions needed for your conclusions.

Based on the analysis:

For lower dosages (0.5 and 1.0 mg), OJ provides more tooth growth than VC;
For 2.0mg dosage tooth growth is teh same for both supplement methods;
Higher dosages give more growth, indepedent of supplemetn method

Project 2 - Statistical Inference - ToothGrowth Analysis

Project Description

1 - Load the ToothGrowth data and perform some basic exploratory data analyses

ToothGrowth {datasets}

2 - Provide a basic summary of the data.

3 - Use confidence intervals and/or hypothesis tests to compare tooth growth by supp and dose. (Only use the techniques from class, even if there’s other approaches worth considering)

4. State your conclusions and the assumptions needed for your conclusions.